Finite element analysis of switching domains using ferroelectric and ferroelastic micromechanical model for single crystal piezoceramics

Here, the domain switching in a ferroelectric and ferroelastic single crystal subjected to electrical, electromechanical, and mechanical loading condition is studied. An isoparametric 3D electromechanical hexahedral finite element introducing the micromechanical constitutive law for domain switching is proposed to investigate the non-linear response of single crystal piezoceramics. The micromechanical model considered here is based on thermodynamic approach and internal variables, accounting for the electromechanical interaction energy between the domains. The volume fractions of six distinct uni-axial variants are treated as the internal variables to describe the microscopic state of the material at any given loading level. Furthermore, the formulation includes a realistic phase transition from a cubic unit cell to tetragonal one in the single crystal piezoceramics under the application of external load. The non-linear electromechanical constitutive equations obtained are solved using an implicit integration technique employing the return-mapping algorithm. The model developed here is tested for its applicability considering variety of benchmarks, and it brings out the behaviour of piezoceramic materials as observed in experimental studies.The hexahedral finite element presented is also implemented in the commercial finite element code Abaqus via the User Element subroutine.